Method of Fundamental Solutions Applied to 3-D Velocity Induced Eddy Current Problems

A meshless method of fundamental solutions (MFS) is applied for the determination of eddy currents inside a translatory moving conductor in the field of a permanent magnet. Three cases are considered: 1) a defect-free specimen; 2) a specimen with a spherical sub-surface defect; and 3) the difference between 1) and 2) as a defect response case. The latter is directly computed with a novel approach using two fictitious surfaces, inside and outside the defect, where the point sources of the MFS are randomly placed. We investigate the optimal distance of the fictitious surfaces containing the randomly placed point sources of the MFS. The eddy current field distributions are compared to a reference finite-element solution. We obtain mean normalized root-mean-square errors below 1% for all three cases. Our proposed meshless MFS for the defect response case allows for direct inclusion into inverse solutions for non-destructive evaluation applications.